Multi-compartment kinetic-allometric model of radionuclide bioaccumulation in marine fish

A model of the radionuclide accumulation in fish taking into account the contribution of different tissues and allometry is presented. The basic model assumptions are as follows: (i) A fish organism is represented by several compartments in which radionuclides are homogeneously distributed; (ii) The compartments correspond to three groups of organs/tissues: muscle, bones and organs (kidney, liver, gonads, etc.) differing in metabolic function; (iii) Two input compartments include gills absorbing contamination from water and digestive tract through which contaminated food is absorbed; (iv) The absorbed 5 radionuclide is redistributed between organs/tissues according to their metabolic functions; (v) The elimination of assimilated elements from each group of organs/tissues differs, reflecting differences in specific tissues/organs in which elements were accumulated; and (vi) The food and water uptake rates, elimination rate and growth rate depend on the metabolic rate, which is scaled by fish mass to the 3/4 power. The analytical solutions of the system of model equations describing dynamics of the assimilation and elimination of Cs, Co, Co, Mn and Zn, which are preferably accumulated in different tissues, 10 exhibited good agreement with the laboratory experiments. The developed multi-compartment kinetic-allometric model was embedded into the compartment model POSEIDON-R, which describes transport of radionuclides in water, accumulation in the sediment, and transfer of radionuclides through the pelagic and benthic food webs. The POSEIDON-R model was applied for the simulation of the transport and fate of Co and Mn routinely released from Forsmark NPP located on the Baltic Sea coast of Sweden and for calculation of Sr concentration in fish after the accident at Fukushima Dai-ichi NPP. Predicted 15 concentrations of radionuclides in fish agree with the measurements much better than predicted using standard whole-body model and target tissue model. The model with the defined generic parameters could be used in different marine environments without calibration based on a posteriori information, which is important for emergency decision support systems

. Distribution of accumulated 137 Cs, 90 Sr and 60 Co in muscle, bone, liver and kidneys according to previously reported data (Yankovich et al., 2010). concentration in the organism relates to the concentration in water using a biological accumulation factor (BAF ). However, to describe highly time dependent transfer processes resulting from accidental releases, dynamic models for the uptake and 25 retention of activity in marine organisms are necessary . According to Takata et al. (2019), the effective recession times of post-Fukushima Dai-ichi Nuclear Power Plant (FDNPP) accident disequilibrium of 137 Cs in biota ranged from 100 to 1,100 days. The most commonly used bioaccumulation models are the whole-body models, where the organism is represented as a single box in which contamination is evenly distributed (e.g. Fowler and Fisher, 2004;Tateda et al., 2013;Vives i Batlle et al., 2016). However, the distribution of radionuclides in organisms, and in particular in fish, 30 is non-uniform. For example, the highest concentration of radiocaesium in fish is observed in the muscle, while the highest concentrations of the actinides, plutonium and americium, are measured in specific organs (Coughtrey and Thorne, 1983).
Moreover, Vives i Batlle (2012) noted that elimination of activity from organisms occurred with different rates that can be interpreted as elimination from different tissues/organs with different metabolism. In a first approximation, this is used in the "target tissue" approach (Heling et al., 2002;Maderich et al., 2014a,b;Bezhenar et al., 2016), where radionuclides are grouped 35 into several classes depending on the type of tissues in which a specific radionuclide accumulates preferentially (target tissue).
However, the contribution of other tissues with greater mass than the mass of the target tissue can be commensurate with the contribution of the target tissue to the amount of radioactivity in the body. This is observed in Fig. 1, which is built from data (Yankovich et al., 2010) where the accumulated activity of 90 Sr in muscle is not negligible in comparison with accumulated activity in bones, whereas the accumulated activity of 60 Co is redistributed between muscle, bone and organs. 40 A more general approach to the description of the radionuclide accumulation in the tissues of fish is using the physiologically based pharmacokinetic (PBPK) models (Barron et al., 1990;Thomann et al., 1997;Garnier-Laplace et al., 2000;Otero-Muras et al., 2010). In the PBPK models, the fish organism is represented as three groups of compartments: absorption compartments simulating uptake of contaminants, distribution compartments simulating tissues and organs, and excretion compartments. The exchange of contaminants between compartments is limited by blood flux perfusing compartments. However, these models 45 require a significant number of parameters depending on elements, fish species and marine environments. They must be determined from the laboratory experiments (Thomann et al., 1997) or by the optimization procedures (Otero-Muras et al., 2010).
Notice that PBPK fish models do not yet include scaling (allometric) relationships between metabolic rates and organism mass (West et al., 1997;Higley and Bytwerk, 2007;Vives i Batlle et al., 2007;Beresford et al., 2016). Therefore, there is a need to develop a generic model of intermediate complexity between the one-compartment model and the PBPK model taking into 50 account (i) the heterogeneity of the distribution of contamination in fish tissues and (ii) the allometric relationships between metabolic rates and organism mass. Such a model can be used for accidental release simulations without local calibration, which is a complicated task in the circumstances of the accident.
In this paper, a new approach for predicting radionuclide accumulation in fish taking into account the contributions of different tissues and allometry is presented. The paper is organized as follows. The model is described in Section 2. The 55 comparison with laboratory experiments is given in Section 3. The results of simulation of several radionuclides in the marine environment for regular and accidental releases are described in Section 4. The conclusions are presented in Section 5.

Model equations
Here, a simple multi-compartmental model to simulate kinetics of radionuclides in the fish is described. The basic assump-60 tions are as follows: (i) a fish organism is represented by several compartments in which radionuclides are homogeneously distributed; (ii) the compartments correspond to three groups of organs/tissues differing in metabolic function: flesh, bones and organs (kidney, liver, gonads, etc.); (iii) two input compartments include gills which absorb contamination from water and digestive tract through which contaminated food is absorbed; (iv) the absorbed radionuclide is redistributed between organs/tissues according to their metabolic functions; (v) the elimination of assimilated elements from each group of organs/tissues differs, reflecting differences in the specific tissues/organs in which elements were accumulated; (vi) the food and water uptake rates, elimination rate and growth rate depend on the metabolic rate, which is scaled by fish mass to the 3/4 power following general theory (West et al., 1997) describing transport of essential materials through space-filling fractal networks of branching tubes in organism.
The equation for concentration of radionuclide [Bq kg −1 wet weight (WW)] in the gill compartment (i = 1) is written as The equation for concentration of unabsorbed radionuclide [Bq kg −1 WW] in the digestive tract compartment (i = 2) is The equations for concentrations of radionuclide [Bq kg −1 WW] in the muscle (i = 3), bones (i = 4) and organs (i = 5) are The activity concentration in the food C f is expressed by the following equation, summing for a total of n prey types where C prey,j is the activity concentration in prey of type 0 ≤ j ≤ n, P j is preference for prey of type j, drw pred is the dry weight fraction of fish, and drw prey,j is the dry weight fraction of prey of type j. The mean whole-body concentration of activity in the organism C wb and whole-body activity A wb [Bq] are calculated as where µ i are weighting factors, ( 5 i=1 µ i = 1). Transfer rates k 1 and k 2 are related with tissue transfer rates k 1i and k 2i as Summing eqns.
(1) to (3) yields the equation for total concentration of activity in fish C wb as where λ g is the organism growth rate, defined as The growth dilution can be ignored in the model calculations when λ g λ i . For short-lived radionuclides, λ i should be corrected taking into account the physical decay. The assimilation efficiencies of elements from water AE w and food AE f 95 (Pouil et al., 2018) can be introduced, assuming that uptake from water and food is equilibrated by loss to the water from gills and through the egestion. The corresponding relations are Taking into account the relations (9)-(10) for constant AE w and AE f , the equation (7) will be similar to the standard whole-100 body single compartment equation  Rouleau et al. (1995) if elimination terms in (7) are replaced by a single term λ wb C wb , assuming that λ wb is a single whole-body elimination rate (Fowler and Fisher, 2004).
The food and water uptake rates, elimination rate and growth rate depend on the metabolic rate, which in turn is known to 105 scale by the organism mass. Here, we employed quarter-power scaling for uptake, elimination and growth rates derived from general theory (West et al., 1997) where α w , α f , α g , α i (i = 1, 5) are constants. These parameters can also depend on temperature, salinity and fish age (e.g. Belharet et al., 2019;Heling and Bezhenar, 2009). Notice that a number of laboratory experiments (Thomas and Fisher, 2010) showed that temperature exerts no major influence on uptake and elimination, whereas the effect of salinity varies for elements (Heling and Bezhenar, 2009;Jeffree et al, 2017). Here, we did not analyze these factors requiring separate consideration.

Kinetics in equilibrium state
The model parameters can be estimated using measurement data and applying the kinetic equations under equilibrium conditions. Equations (1) -(3) rewritten for radionuclide concentrations in the equilibrium state are 120 Then, using (13)-(14), the assimilation efficiencies of elements from water AE w and food AE f are rewritten as When λ 1 λg, λ 2 λg, we determine from (16) and (12), approximately, The equations under (17) is used to relate kinetic coefficients of the model with experimentally determined parameters AE w , AE f , λ 1 and λ 2 . The equations under (15) can be rewritten as where AE wi and AE f i are assimilation efficiencies for tissue i, The assimilation efficiencies are expressed through kinetic coefficients as The bioaccumulation factors for food BAF f ood , for whole-body of fish BAF wb and body-to-tissue concentration ratio CR i are described as Values of BAF for different radionuclides are available in IAEA (2004). Yankovich et al. (2010) provide CR i based on aggregate experimental data for marine fish. Assume that the kinetics of assimilation in fish tissues are similar for radionuclides absorbed from water and food, i.e.  (Pouil et al., 2018), tissue assimilation efficiencies AE f i and T T F for several elements. Notice that assimilation for some elements can be considered as route dependent (Reinfelder et al., 1999), and so (22) is only a first approximation. Inserting (22) into (18) yields Summing (23) for i = 3, 4, 5 yields 145 Using (23) and (24), ratio AE f i /AE f can be written as The values of kinetic coefficients k 1 , k 2 and assimilation efficiencies for tissues AE f i were calculated from (17) and (25) using assimilation efficiencies from experimental data (Pouil et al., 2018). The values of AE f i for several radionuclides are given in Table 2. Equation (24) can be rearranged to express the ratio of BAF wb to BAF f ood taking into account dominance of dietary 150 intake over water intake (Mathews and Fisher, 2009). This ratio is the trophic transfer factor (T T F ), written as A T T F > 1 indicates possible biomagnification, and T T F < 1 indicates that biodiminution is likely. As follows from (26), the T T F value does not depend on the mass of fish. The T T F values calculated by using (26) are given in Table 2. Among the considered elements, only caesium (T T F > 1) may be biomagnified in the food chain, in agreement with Kasamatsu and 155 Ishikawa (1997), where it was found that the BAF of 137 Cs increased with increasing trophic level. The concentrations of other radionuclides in Table 2 decreased with the increase of trophic level (T T F < 1), which is consistent with the findings presented by Cardwell et al. (2013), where an inverse relationship was obtained between trophic levels and the concentration of inorganic metals in water chains.
Notice that values of AE f , AE w and BAF do not depend on the fish mass. The literature data reveal diverse relationships 160 between fish mass and both radionuclide bioconcentration (BCF ) and bioaccumulation (BAF ) factors. In particular, data of laboratory experiments  showed that there is no significant relationship between bioconcentration factor BCF and fish size for most studied aqueous metals. The BAF in larger and older fish of the same species can differ from smaller and younger fish due to the change of habitat and diet with age (e.g. Kasamatsu and Ishikawa, 1997;Ishikawa et al., 1999;Kim et al., 2019) that does not contradict our findings.

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3 Comparison with laboratory experiments 3.1 Depuration of radionuclides after pulse-like feeding Retention of absorbed elements in fish after single feeding was often used to estimate AE f and depuration rate (e.g. Jeffree et al., 2006;Pouil et al., 2017). According to Goldstein and Elwood (1971), single feeding can be approximated by a delta function δ(t) at t = 0 as where A f is the total amount of ingested activity. The solutions of equations (1)-(3) for activities A 2 = m 2 C 2 and A i = m i C i and for initial conditions A

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As follows from solutions (28) The solutions (28)-(29) can be compared with laboratory experiments in which depuration of metals from the fish after single feeding was studied. In the experiment by , the retention of several radioisotopes in juvenile sea bream (Sparus auratus) was considered. The average wet weight of the fish was 0.0001 kg. These fish were fed radiolabelled Artemia salina nauplii. The fish were allowed to feed for one hour, after which metal retention was observed in clean water  The solutions were also compared with laboratory experiments for predator fish . In these experiments, 190 the retention of several radioisotopes in sea bream (Sparus auratus), turbot (Psetta maxima) and spotted dogfish (Scyliorhinus canicula) was studied. Immature S. auratus (wet weight 0.012 kg), P. maxima (wet weight 0.027 kg), and S. canicula (wet weight 0.008 kg) were fed radiolabelled prey fish (juvenile S. auratus). After this feeding, fish were fed unlabelled prey fish for three weeks. In Fig. 3, the solutions (28)-(29) were compared with the laboratory experiments in which prey fish were labelled by 134 Cs, 57 Co, 54 Mn, and 65 Zn. The solution (28)-(29) and experiment agreed, demonstrating general dependence of 195 the depuration process on fish mass. Differences between experimental data for different species may be due to differences in anatomy and physiology, as discussed by Jeffree et al. (2006) for P. maxima and S. canicula. The model, unlike the situation for prey fish (Fig. 2), underestimates the total concentrations of 57 Co and 54 Mn in comparison with experiments, which is probably due to the neglect of other factors, except body weight, for the bioaccumulation kinetics.

Bioconcentration of dissolved radionuclides from sea water 200
Uptake and absorption in fish of elements from water were studied in several laboratory experiments (e.g. Jeffree et al., 2006;. The modelling of the absorption of elements can be used to estimate an assimilation efficiency AE w . An analytical solution of equations (1) and (3) with initial conditions C i = 0 at t = 0 is written as These solutions were compared with laboratory experiments for prey fish  and for predator fish (Jeffree et al., 2006). In the experiment by , the uptake of several radioisotopes by juvenile S.  Fig. 4. The values of AE w were selected to approximate the experiment for small prey fish  in experiments by Jeffree et al. (2006). As seen in Fig. 4, values of AE w for considered elements are of the order 10 −3 , which is in agreement with most models. However, comparison with larger fish highlighted some differences between species of fish, as discussed by Jeffree et al. (2006), and differences between model and experiment for a constant value of AE w . At the same time, it is known that dietary intake of metals dominates over water intake (Mathews and Fisher, 2009). Therefore, deviations in values of AE w would not be significantly affected by the full uptake of elements from the marine environment.

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The parameter α 1 can be estimated from the relations (13) and (16) according to the experimental data for equilibrium condi- tions. An average value of gill BCF 1 is approximately 10 l kg −1 for 58 Co, 54 Mn, 134 Cs and 65 Zn (Jefferies and Heweit,1971;Pentreath, 1973). Then for AE w =0.001 we obtained α 1 =0.8. With the selected value of α 1 , the process of adaptation of the gill tissue to changes in the concentration of radioactivity in water is much faster than for other tissues of the fish. In addition, as follows from the solution (30)-(31) at λ 1 λ i , the contribution of gill contamination to the whole-body contamination is 225 small.

Simplification of the model based on the results of analytical solutions and laboratory experiments
Comparison of the model with laboratory experiments on the retention of absorbed elements in fish after single feeding has shown the importance of including in the model of the digestive tract compartment describing highly non-equilibrium transfer dynamics. However, for modelling of food uptake in marine environment with multiple feedings the simple equilibrium 230 assumption (14) can be used. At the same time, the analytical solution describing the bioconcentration due to the uptake and absorption in fish of elements from water, as well as the results of the laboratory experiment, show that the contribution to the gills (13) is negligible. Therefore, for modelling of uptake from water the equilibrium assumption can also be used as it shown above. The corresponding simplified equations for muscle, bone and organs can be rewritten as

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The uncertainty in calculations using equations (32) arises due to (i) limited experimental data to define allometry constants α f , α w , α 3 , α 4 , α 5 ; (ii) large intervals in the values of known AE f coefficients; (iii) unknown AE f values for many radionuclides; (iv) lack of experimental data about AE w ; (v) limited experimental data for whole-body to tissue concentration ratios CR i in the marine fish. Therefore, a sensitivity analysis is necessary to estimate uncertainty of the simulation results. We estimated the effects of variations in above parameters in the equation (24) on the value of BAF wb in equilibrium state. The simple local 240 sensitivity analysis and One-At-a-Time method (Pianosi et al., 2016) was used. The sensitivity of model output was estimated using a sensitivity index (SI) calculated following Hamby (1994)as where D max and D min are the outputs corresponded to maximal and minimal input parameter values, respectively. Similarly to Bezhenar et al. (2016), the range for every parameter was defined as follows: minimum value was set to half the reference 245 value and maximum value was set to twice the reference value. Calculated SI for three radionuclides, which are preferably accumulated in different tissues: 137 Cs, 90 Sr, and 60 Co, are given in Table. S2.
The results of sensitivity study suggest that model results are most sensitive to variations of AE f and α f for 137 Cs and 60 Co, whereas for 60 Co they are almost not sensitive to variations of AE w and α w . Note that model results are also sensitive to the variations of parameters related to tissues where radionuclide is mainly accumulated: α 3 and CR 3 for 137 Cs, α 5 and CR 5 for

Modified compartment POSEIDON-R model
In order to predict the accumulation of radionuclides in fish in the marine environment using the multi-compartment kineticallometric (MCKA) model described above, it is necessary to calculate changes in concentration in water and in bottom sedi-255 ments and to calculate the transport of radionuclides through food chains. The POSEIDON-R compartment model (Lepicard et al., 2004;Maderich et al., 2014a,b;2018b;Bezhenar et al., 2016) can be used to simulate the marine environment as a system of 3D compartments for the water column, bottom sediment, and food web. The water column compartment is vertically subdivided into layers. The suspended matter settles in the water column. The bottom sediment compartment is divided into three layers (Fig. S1). The downward burial processes operate in all three sediment layers. Maderich et al. (2018b) described the 260 POSEIDON-R compartment model in detail. A food web model that includes pelagic and benthic food chains is implemented within the POSEIDON-R compartment model . In the food web model, marine organisms are grouped into classes according to trophic level and species type (Fig. S2). The food chains differ between the pelagic zone and the benthic zone. Pelagic organisms comprise primary producers (phytoplankton) and consumers (zooplankton, non-piscivorous Figure 5. Compartment system around the Forsmark NPP. The numbers denote regional boxes in the box system of the Baltic Sea ). An additional "Inner box" is separated from regional box 68 by the blue line. The coastal box (red rectangle) surrounds the area, where cooling water from NPP is discharged.
(forage) fish, and piscivorous fish). In the benthic food chain, radionuclides are transferred from algae and contaminated bottom 265 sediments to deposit-feeding invertebrates, demersal fish, and benthic predators. Bottom sediments include both organic and inorganic components. Radioactivity is assumed to be assimilated by benthic organisms from the organic components of the bottom deposits. Other food web components are crustaceans (detritus feeders), molluscs (filter feeders), and coastal predators, which feed throughout the water column in shallow coastal waters. All organisms take in radionuclides both via the food web and directly from the water. Details of the transfer of radiocaesium through the marine food web are presented by Bezhenar et

Release of radionuclides during normal operation of the Forsmark nuclear power plant
This section presents the simulation results of 60 Co and 54 Mn routine release into the marine environment from Forsmark NPP, located on the Baltic Sea coast of Sweden. The compartment POSEIDON-R model with embedded food web MCKA model, one-compartment model and bioaccumulation factor (equilibrium) model was customized for the Baltic Sea, as described by 275 Bezhenar et al. (2016) and Maderich et al. (2018a). A set of nested boxes inside the regional box no. 68 in the Baltic Sea box system was added to resolve the near field of radionuclide concentration (Fig. 5). Parameters of the "inner box" and "coastal box" are based on data from (SKB, 2010). The main parameters of boxes with zooming in to the NPP are presented in Table S3 Figure 6. Release rates of 60 Co and 54 Mn according to measurements (Forsmark, 2014).
in the Supplement. The simulation results for 60 Co and 54 Mn were compared with measurements for the smallest coastal box, where measurement data for bottom sediments and fish were available (Forsmark, 2014). The measurement data were compared 280 with simulations for two species of fish: herring (Clupea harengus membras) as a non-piscivorous fish and pike (Esox lucius) as a coastal predator. There is no information on the mass of fish caught in the vicinity of Forsmark NPP. Therefore, we used estimates of the masses typical for prey and predatory fish, which are given in Table S1. In the one-compartment model, two parameters must be prescribed: assimilation efficiency and biological half-life T 0.5 = ln2λ −1 wb . Assimilation efficiency (see Table 2) was obtained from Pouil et al. (2018). Baudin et al. (1997) used T 0.5 = 21 d for 60 Co in the one-compartment model.

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The average value for T 0.5 in predatory marine fish is 40 d (Beresford et al., 2015). Therefore, for 60 Co, we used T 0.5 = 20 d for prey fish and T 0.5 = 40 d for predatory fish. There are very limited data for T 0.5 values in marine fish for 54 Mn. According to Beresford et al. (2015), T 0.5 is in the range between 20 and 40 days. Therefore, we used the same values of T 0.5 for 54 Mn, as for 60 Co.
The release rates of 60 Co and 54 Mn from the Forsmark NPP (Forsmark, 2014) are plotted in Fig. 6. As seen in Fig. 7a,   290 the results of simulation for the concentration of 60 Co in the bottom sediments are in good agreement with the measurements (Forsmark, 2014) in the coastal box for the wide range of employed values of sediment distribution coefficient K d : from K d = 3 · 10 5 ÷ 2 · 10 6 L kg −1 for margin seas to K d = 5 · 10 7 L kg −1 for open ocean (IAEA, 2004). The benthic food web (Bezhenar et al., 2016a), which describes the transfer of radioactivity from bottom sediments to deposit-feeding invertebrates and finally to fish, is quite important in this range of K d values. The results from the POSEIDON-R calculations obtained with 295 the MCKA model are compared (Fig. 7b,c) with measurements and results of calculations obtained with a one-compartment model and with an equilibrium approach using a standard BAF value (IAEA, 2004). Whereas one-compartment and equilibrium models underestimated the concentration of 60 Co in fish, the MCKA model using generic parameters yields better agreement with measurements for both non-piscivorous fish (Fig. 7b) and coastal predator feeding by pelagic and benthic organisms in the coastal area (Fig. 7c).

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Similarly, the behaviour of 54 Mn in the marine environment near the Forsmark NPP is modelled. The release rate of 54 Mn from the NPP is also plotted in Fig. 6 using data from Forsmark (2014). Comparison of the simulated concentration of 54 Mn in bottom sediments with measurements (Forsmark, 2014) for the Forsmark coastal box is given in Fig. 8a. Good agreement was obtained when a standard value of K d = 2 · 10 6 L kg −1 for 54 Mn in margin seas (IAEA, 2004) was used. This means that, as in the case of 60 Co, a significant fraction of radionuclide is deposited at the bottom, and the benthic food web should 305 be considered. Similarly to the 60 Co case, obtained results of simulation are also compared with results obtained using the one-compartment model and equilibrium approach. Again, the MCKA model yields the best agreement with measurements for both non-piscivorous fish (Fig. 8b) and coastal predators (Fig. 8c); however, this agreement is slightly worse than in the 60 Co case. Notice that the BAF in the equilibrium approach can be locally estimated using a posteriori data. However, the MCKA model provided good agreement with measurements using only a priori information, which is important in the case of 310 accidents, as considered in the next section.

Accumulation of 90 Sr in the fish after the Fukushima Dai-ichi accident
Following caesium, 90 Sr is the second most important radiologically long-lived radionuclide released as a result of the FDNPP accident. It is highly soluble in water and exhibits relatively high ability for assimilation by marine organisms due to similar chemical properties with calcium. The atmospheric deposition of 90 Sr is usually not taken into account due to its low volatility.

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Most of the 90 Sr released from the FDNPP was directly released to the ocean, with estimates of total inventory in the range from 0.04 to 1.0 PBq (Buesseler et al., 2017). Here, we extended the simulation by Maderich et al. (2014b) of transfer and fate of 90 Sr resulting from the FDNPP accident using the POSEIDON-R model complemented by the food web model ) and MCKA fish model.  The POSEIDON-R model was customized for the Northwestern Pacific and adjacent seas (the East China Sea, the Yellow 320 Sea and the East/Japan Sea) as in (Maderich et al., 2018a). A total of 188 compartments covered this region. The compartments around the FDNPP are shown on Fig. 9 with an additional 4x4 km coastal box in the vicinity of FDNPP. The coastal box was  The historical contamination due to global atmospheric deposition in the period from 1945-2010 was simulated according 325 to (Maderich et al., 2014b) with data from the MARiS database (2020). The value of the accidental release was estimated as 160 TBq (16 TBq day −1 during 10 days), that was consistent with the range reported by Buesseler et al. (2017). In the post-accidental period, the continuous leakage of 90 Sr due to groundwater transport of radioactivity from the NPP site was monitored (Castrillejo et al., 2016). Therefore, in the simulation the conservative scenario was used for release of 90 Sr in the post-accidental period (Fig. 9); the release of 90 Sr was assumed equal to 137 Cs release (Maderich et al. (2018a). Comparison 330 between calculated and measured 90 Sr concentrations in water, bottom sediment, and piscivorous fish for the coastal box and box no. 173 are shown in Figs. 10 and 11, respectively. Measured concentrations of 90 Sr in the water and bottom sediments before the accident were obtained from the MEXT database (MEXT, 2020). Concentrations of 90 Sr after the accident at TEPCO (Tokyo Electric Power Company) sampling points near the discharging canals (T1 and T2) and at different distances offshore (TD-5 inside the coastal box area, T7, TD-1 and TD-9 for outer box no. 173) are available in the NRA (Nuclear Regulation between calculated and measured concentrations (Figs. 10a, 11a) could be a confirmation of the correctness of estimation of the source term. This is also confirmed by agreement of measured and simulated concentrations of 90 Sr in the bottom sediment ( Fig. 10b). Notice that there is no measurement data for bottom sediment in box no. 173 (Fig. 11b).
The calculated concentration of 90 Sr in piscivorous fish was compared with measurement data for fat greenling (Hexagrammos otakii) before the accident (JCAC, 2020) and with data from (NRA, 2020) and Miki at al. (2017) after the accident. The

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NRA data for 90 Sr are very limited. Therefore, different species of piscivorous fish were considered, such as sharks (Triakis scyllium, Squatina japonica), rockfish (Sebastes cheni) and seabass (Lateolabrax japonicus). The simulation results with the MCKA model agree well with the experimental observations (Fig. 10c,11c), while the target tissue (TT) approach underestimates the concentration of 90 Sr in the fish.

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A new approach to predicting the accumulation of radionuclides in fish taking into account heterogeneity of distribution of contamination in the organism and dependence of metabolic process rates on the fish mass was developed. The fish organism was represented by compartments for three groups of tissues/organs (muscle, bone, organs) and two input compartments representing gills and digestive tract. The absorbed elements are redistributed between organs/tissues and then eliminated according to their metabolic function. The food and water uptake rates, elimination rate and growth rate depend on the metabolic rate, 355 which is scaled by fish mass to the 3/4 power. This model is of intermediate complexity and provides an alternative for the basic/simplistic whole-body models and the highly advanced PBPK models.
The trophic transfer factors (T T F ) were calculated for 9 elements using assimilation efficiencies AE f obtained from laboratory data. Among considered elements, only caesium (Cs) may biologically magnify when transferring upwards into the food chain (T T F > 1). This is in agreement with measurements. The concentrations of other elements (Sr,Co,Mn,Zn,Ag,360 Cu, Cd, and Cr) decrease with the increase of trophic level (T T F < 1). The kinetics of the assimilation and elimination of 134 Cs, 57 Co, 60 Co, 54 Mn and 65 Zn, which are preferably accumulated in different tissues, were analyzed using the analytical solutions of a system of model equations. These solutions exhibited good agreement with the laboratory experiments for the depuration process after single feeding of fish with radiolabelled prey and with respect to uptake of activity from water. Notice that for relatively slow processes in the marine environment, transfer processes in the gills and digestive tract can be close to 365 equilibrium, which allows consideration of only a three-compartment (muscle, bone, organs) version of the model. The developed MCKA model was embedded into the compartment model POSEIDON-R, which describes the transfer of radionuclides through the pelagic and benthic food webs. The POSEIDON-R model was applied for the simulation of the